Measurement of dispersion and variation have been studied and evaluated in many applications. Volatility in the field of finance is an important measure as it directly impacts allocation, risk management, and valuation. Pitman Closeness criterion is used to compare estimators of standard deviation from equity returns in a control charting application. Three estimators are evaluated over the 30 DJIA component stocks in an effort to determine if one method of estimation has better performance within an application of control charting for identifying outliers. The study uses three sample sizes to also determine if the better estimator is sample size dependent.
Market Volatility has been investigated at great lengths, but the measure of historical volatility, referred to as the relative volatility, is inconsistent. Using historical return data to calculate the volatility of a stock return provides a measure of the realized volatility. Realized volatility is often measured using some method of calculating a deviation from the mean of the returns for the stock price, the summation of squared returns, or the summation of absolute returns. We look to the stocks that make up the DJIA, using tick-by-tick data from June 2015 - May 2016. This research helps to address the question of what is the better measure of realized volatility? Several measures of volatility are used as proxies and are compared at four estimation time intervals. We review these measures to determine a closer/better fit estimator to the true realized volatility, using MSE, MAD, Diebold-Mariano test, and Pitman Closeness. We find that when using a standard deviation based on transaction level returns, shorter increments of time, while containing some levels of noise, are better estimates of volatility than longer increments.
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